Screw closures of the kind addressed herein are known. They either present an inner thread that meshes with the outer thread of a container or they are bayonet locks. In both cases, it is critical that to be opened the screw closure undergo a certain rotatory motion and particularly an axial transverse motion, whereby the closure is lifted from the container or its mouth. It is known to provide such screw closures with a security band, also known as warranty band, which upon the first opening, namely when the screw closure is taken off the container for the first time, is deformed or destroyed in certain regions so that the outer contour is changed. As a result of the changed outer contour, a user can immediately recognize that the container is no longer closed in the original manner and that it possibly has been tampered with. It has been found that the first opening of a screw closure requires rather high opening forces, to prevent easy opening of the closure. Moreover, for many closures of this kind the force needed to reclose the container is relatively high. Finally, in many cases the deformed security band interferes with reclosure. In the known closures, the warranty band is connected to a predetermined breaking line extending all around in the circumferential direction and is provided with a separation line extending vertically thereto. When the closure is opened for the first time, the predetermined breaking line is split in some parts, and the separation line opens up.